11-1

Chapter 1Chapter 1

21-2

Chapter One

What is Statistics?What is Statistics?

ONEUnderstand why we study statistics.TWOExplain what is meant by descriptive statistics and inferential statistics.THREEDistinguish between a qualitative variable and a quantitative variable.FOUR Distinguish between a discrete variable and a continuous variable.FIVEDistinguish among the nominal, ordinal, interval, and ratio levels of measurement.SIXDefine the terms mutually exclusive and exhaustive.

GOALSWhen you have completed this chapter, you will be able to:

31-3

Why study statistics?

• Numerical info is everywhere– But how do we know if conclusions reported are accurate?

• Statistical techniques are used to make decisions that affect our lives– This is why younger people pay more for insurance…

• Knowledge of statistical methods at least helps you understand why decisions are made – In future you will make decisions that involve data

41-4

What is Meant by Statistics?

Statistics is the science of collecting, organizing, presenting, analyzing, and interpreting numerical data to assist in making more effective decisions.

In common usage statistics refers to numerical information….. But in this course the term has a wider meaning….

51-5

Who Uses Statistics?

Statistical techniques are used extensively by managers in marketing, accounting, quality control, consumers, professional sports people, hospital administrators, educators, politicians, physicians, gamblers, etc...

61-6

Types of StatisticsDescriptive Statistics: Methods of organizing, summarizing, and presenting data in an informative way.

EXAMPLE 1: A Gallup poll found that 49% of the people in a survey knew the name of the first book of the Bible. The statistic 49 describes the number out of every 100 persons who knew the answer.

71-7

Types of StatisticsDescriptive Statistics: Methods of organizing, summarizing, and presenting data in an informative way.

EXAMPLE 2: According to Consumer Reports, General Electric washing machine owners reported 9 problems per 100 machines during 2002. The statistic 9 describes the number of problems out of every 100 machines.

81-8

Types of StatisticsDescriptive Statistics: Methods of organizing, summarizing, and presenting data in an informative way.

EXAMPLE 3: The Canadian government reports that the population of Canada was 18,238,000 in 1961, 21,568,000 in 1971, 24,820,000 in 1981, 28,031,000 in 1991, and 31,050,700 in 2001. If we calculate percentage growth over the decades it is also descriptive statistics.

91-9

Types of Statistics Inferential Statistics: The methods used to determine something about a population, based on a sample.

O EXAMPLE 1: In the preceding example on Canadian population changes, if you use the past data to forecast the population of Canada in the year 2010 or expected percentage of growth from 2000 to 2010, then this is considered inferential statistics.

101-10

Types of Statistics Inferential Statistics: The methods used to determine something about a population, based on a sample.

EXAMPLE 2: The accounting department of a large firm will select a sample of the invoices to check for accuracy for all the invoices of the company.

111-11

Types of Statistics Inferential Statistics: The methods used to determine something about a population, based on a sample.

EXAMPLE 3: Wine tasters sip a few drops of wine to make a decision with respect to all the wine waiting to be released for sale.

121-12

Population vs. Sample

Population is the entire set of individuals or objects of interest or the measurements obtained from all individuals or objects of interest.

Sample is a portion, or part, of the population of interest

131-13

See also p.7

Population: All items

Sample: Items selected from the population

141-14

NB: don’t confuse population in statistics with a country’s population!

• A population might consist of all the people in Nanaimo but also may mean the PE ratios for all chemical stocks, or total assets of the 20 largest banks in North America, total collection of prices, ages, square footage of retail space in Nanaimo, and so on.

151-15

Types of Variables

For a Qualitative or Attribute variable the characteristic being studied is nonnumeric.

EXAMPLES: Gender, religious affiliation, type of automobile owned, country of birth, eye colour are examples.

161-16

Types of Variables

In a Quantitative variable information is reported numerically.

EXAMPLES: balance in your cheque account, minutes remaining in class, or number of children in a family.

171-17

Types of VariablesQuantitative variables can be classified as either discrete or continuous.

Discrete variables: can only assume certain values and there are usually “gaps” between values.

EXAMPLE: the number of bedrooms in a house, or the number of hammers sold at the local Home Depot (1,2,3,…,etc). But you cannot have 2.3 bedrooms or 10.6 hammers…Thus discrete variables result from counting.

181-18

Types of Variables

A continuous variable can assume any value within a specified range.

Examples are: The pressure in a tire, the weight of a pork chop, or the height of students in a class. Typically, continuous variables are the result of measuring something.

191-19

Summary of Types of Variables

Q u a lita t ive o r a ttrib u te(typ e o f ca r ow n ed )

d isc re te(n u m b er o f ch ild ren )

con tin u ou s(t im e taken fo r an exam )

Q u an tita tive o r n u m erica l

D A TA

201-20

Levels of Measurement• Data may be classified into four classes or levels of

measurement: nominal, ordinal, interval, and ratio.

Nominal level: Data that is classified and counted.

EXAMPLES: eye colour, gender, religious affiliation.

211-21

Levels of Measurement

Mutually exclusive: An individual, object, or measurement is included in only one category.

Exhaustive: Each individual, object, or measurement must appear in one of the categories.

Nominal data have no particular order or rank and are mutually exclusive.

221-22

Marital Status 2000 (population 15 years and older)

Status Number

Single (never married) 7,285,560

Married (legally, separated, common-law)

14,614,564

Divorced 1,452,000

Widowed 1,527,075

Total 24,879,199

These data are a nominal level of measurement because it can only be classified into classes and the order of the marital status is not important. The classes are also mutually exclusive and exhaustive.

231-23

Levels of MeasurementOrdinal level: involves data arranged in some order, but the differences between data values cannot be determined or are meaningless.

EXAMPLE: During a taste test of 4 soft drinks, Mountain Dew was ranked number 1, Sprite number 2, Seven-up number 3, and Orange Crush number 4.

241-24

Levels of MeasurementInterval level is similar to the ordinal level, with the additional property that meaningful amounts of differences between data values can be determined. There is no natural zero point.

EXAMPLE: Temperature on the Celsius scale. 0 degrees does not represent the absence of temperature, just that it is cold!

251-25

Levels of Measurement

Ratio level is the interval level with an inherent zero starting point. Differences and ratios are meaningful for this level of measurement.

EXAMPLES: Monthly income of surgeons, or distance traveled by manufacturer’s representatives per month.

261-26

Chapter 1 - Practice Quiz

1 Which word is not part of the definition of statistics?

A) Organizing

B) Analyzing

C) Presenting

D) Predicting

2 In descriptive statistics our main objective is to

A) Describe the population.

B) Describe the data we collected.

C) Infer something about the population.

D) Compute an average.

271-27

3 Which of the following statements is true regarding a population?

A) It must be a large number of values.

B) It must refer to people.

C) It is a collection of individuals or objects.

D) None of the above.

4 Which of the following statements is true regarding a sample?

A) It is part of population.

B) It must contain at least five observations.

C) It refers to descriptive statistics.

D) All of the above are correct.

281-28

5 A qualitative variable

A) Always refers to a sample.

B) Is not numeric.

C) Has only two possible outcomes.

D) All of the above are correct.

6 A discrete variable is

A) An example of a qualitative variable.

B) Can assume only whole number values.

C) Can assume only certain clearly separated values.

D) Cannot be negative.

291-29

7 A nominal scale variable is

A) Usually the result of counting something.

B) Has a meaningful zero point.

C) May assume negative values.

D) Cannot have more than two categories.

8 The ratio scale of measurement

A) Usually involves ranking.

B) Cannot assume negative values.

C) Has a meaningful zero point.

D) Is usually based on counting.

301-30

9 The ordinal scale of measurement

A) Has a meaningful zero point.

B) Is based on ranks.

C) Cannot assume negative values.

D) All of the above.

10 Categories are exhaustive when

A) There is a meaningful zero point.

B) The objects can be ranked.

C) Each object must appear in at least one category.

D) Each object can be included in only one category.